JP6926978B2 - Parameter estimator, trip predictor, method, and program - Google Patents

Description

The present disclosure relates to parameter estimators, trip predictors, methods, and programs.

Trip prediction plays an important role in optimizing ride-sharing systems such as taxi, car-sharing, and bike-sharing. For example, if the trip of a car in a car sharing system can be predicted, the car can be arranged in advance at a time or a point where riding needs are high.

Techniques for predicting trips can be divided into two categories. The first category is micromodels. For example, Non-Patent Document 1 describes a method of modeling a sequence of departure time and arrival time of each trip using a point process.

The second category is macro models. The macro model divides the time axis into a plurality of time slots and models the number of departure trips and the number of arrival trips for each time slot. For example, Non-Patent Document 2 and Non-Patent Document 3 propose a method of modeling by a clustering-based method.

Alvarez-valdes, R .; Belenguer, J. M .; Benavent, E .; Bermudez, J. D .; Vercher, E .; and Verdejo, F. 2015. Optimizing the level of service quality of a bike-sharing system, Omega. Yang, Z .; Hu, J .; Shu, Y .; Cheng, P .; Chen, J .; and Moscibroda, T. 2016. Mobility Modeling and Prediction in Bike-Sharing Systems. MobiSys 2016 165178. Liu, J .; Sun, L .; Chen, W .; and Xiong, H. 2016. Rebalancing Bike Sharing Systems: A Multi-source Data Smart Optimization. Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining KDD '16 10051014.

The method described in Non-Patent Document 1 can capture the temporal periodicity of trip demand, but does not consider external information such as weather. Previous studies have confirmed that trip demand fluctuates significantly due to the influence of external factors such as weather (for example, Non-Patent Document 2 and Non-Patent Document 3).

On the other hand, the methods described in Non-Patent Document 2 and Non-Patent Document 3 can incorporate external information such as temporal periodicity and weather, but do not consider temporal continuity, so that the trend changes (time evolution). I can't catch. Further, since the methods described in Non-Patent Document 2 and Non-Patent Document 3 aggregate trips, information associated with each trip (user profile, trip type, etc.) cannot be considered.

Furthermore, there is no method that considers all four elements of the above-mentioned external information such as temporal periodicity, trend, and weather, and information associated with each trip. Therefore, it is not possible to properly model the trips affected by these, and there is a problem that the accuracy of prediction is lowered. For example, if the overall demand increases over time, accurate forecasts cannot be made without considering trends.

The present disclosure has been made in view of the above points, and an object of the present disclosure is to provide a parameter estimation device, a trip prediction device, a method, and a program capable of realizing highly accurate prediction of future trips. do.

In order to achieve the above object, the parameter estimation device of the first aspect of the present disclosure uses the trip history information and the external information affecting the trip to set the departure time and the arrival point for each arbitrary point. It is a departure model that models the departure event defined in the set using a point process model, and estimates the parameters that optimize the departure model expressed by the intensity function that represents the probability that the departure event will be generated per unit time. Then, using the trip history information, a parameter for optimizing the trip time model in which the change in the trip time from the departure point to the arrival point is learned for each arbitrary point is estimated.

In order to achieve the above object, the parameter estimator of the second aspect of the present disclosure is modeled in the parameter estimator of the first aspect by changing the intensity function linearly with time. It has a time-dependent term, including a trend term, which is a term.

The parameter estimator of the third aspect of the present disclosure is the parameter estimator of the first or second aspect, wherein the intensity function includes a periodic term which is a term modeled by superposition of kernel functions. , Has a time-dependent term.

In the parameter estimation device of the fourth aspect of the present disclosure, in the parameter estimation device of any one of the first to third aspects, the parameter for optimizing the trip time model is included in the trip history information. It is estimated according to the probability distribution of the trip time between arbitrary points for each auxiliary information.

In order to achieve the above object, the trip prediction device of the fifth aspect of the present disclosure is optimized by the parameters estimated by the parameter estimation device according to any one of the first to fourth aspects. It is provided with a prediction unit that predicts a future trip at an arbitrary point based on the departure model and the trip time model optimized by the parameters estimated by the parameter estimation device.

In order to achieve the above object, the method of the sixth aspect of the present disclosure is a combination of a departure time and an arrival point for each arbitrary point using trip history information and external information affecting the trip. Parameters that optimize the modeled departure model by expressing the defined departure event with an intensity function that represents the probability that the departure event will be generated per unit time using a marked point process marked with the arrival time. This is a parameter estimation method that estimates and uses trip history information to estimate parameters that optimize a trip time model that has learned changes in trip time.

In order to achieve the above object, the method of the seventh aspect of the present disclosure is estimated by a starting model optimized by the parameters estimated by the parameter estimation method according to the sixth aspect and the parameter estimation method. It is a trip prediction method that predicts a future trip at an arbitrary point based on a trip time model optimized by the parameters.

In order to achieve the above object, the program of the eighth aspect of the present disclosure is for causing the computer to function as the parameter estimation device according to any one of the first to fourth aspects. ..

According to the present disclosure, it is possible to realize a highly accurate prediction of future trips.

It is a block diagram which shows the structure of an example of the trip prediction apparatus of embodiment. It is a figure which shows an example of the trip history information of an embodiment. It is a figure which shows an example of the external information of an embodiment. It is a flowchart which shows an example of the parameter estimation routine executed by the parameter estimation apparatus of the trip prediction apparatus of embodiment. It is a flowchart which shows an example of the trip prediction routine executed by the trip prediction apparatus of embodiment.

The present disclosure relates to a technique for predicting future trips based on trip history and external information affecting trips. Hereinafter, the present embodiment will be described in detail with reference to the drawings. The present embodiment does not limit the present disclosure.

<Overview>
In this disclosure, we propose a method for predicting trips in the near future while considering the influence of external factors by extending the point process model to a form that can handle external information that affects trips. In the present embodiment, the trip is a movement by a person from one point to another and a vehicle such as a bicycle or a car, and the departure point, departure time, arrival point, and arrival time, which will be described in detail later. It is represented by a combination.

The technique of the present disclosure consists of two modules, a departure model and a trip time model. The departure model is a model of a series of pairs of departure time and arrival point at an arbitrary point using a marked point process. In the departure model, the arrival time is regarded as a mark, and the marked point process is extended to take external information into consideration to capture changes in trip demand due to external factors such as weather. On the other hand, the trip time model learns external information such as time and weather, and the relationship between the information associated with each trip and the trip time from the data.

The arrival time at an arbitrary point can be estimated based on the departure time and arrival point estimated by the departure model and the trip time estimated by the trip time model.

<Configuration of trip prediction device>
Next, the configuration of the trip prediction device of the present embodiment will be described with reference to the drawings. FIG. 1 is a block diagram showing a configuration of a trip prediction device.

As shown in FIG. 1, in the present embodiment, the trip history storage device 12 and the external information storage device 14 are provided outside the trip prediction device 10. The trip history storage device 12 and the external information storage device 14 may be provided in the trip prediction device 10, not limited to the present embodiment.

The trip history storage device 12 stores trip history information (trip history information) 13 that can be analyzed by the trip prediction device 10. The trip history storage device 12 reads the trip history information 13 in accordance with the request from the trip prediction device 10, and transmits the read trip history information 13 to the trip prediction device 10.

The trip history information 13 is, for example, data representing the movement of a bicycle, a person, or the like, and is a tuple (u, v, t, which includes a departure point u, an arrival point v, a departure time t, an arrival time τ, and auxiliary information m. It is defined by τ, m). Here, the auxiliary information is variables associated with each trip, such as trip type, user attributes, and user type. Examples of the type of trip include whether the trip is one-way or round-trip. In addition, examples of the user's attributes include the age and gender of the user. Examples of the user type include whether the ride sharing system is a member or a non-member of the system.

FIG. 2 shows an example of trip history information 13. The trip history information 13 shown in FIG. 2 shows a case where a user type (member / non-member) is used as an example of auxiliary information.

について、Ｋ個のバイク地点（以下、単に「地点」という）からなる組、Ｓ＝｛ｓ_１，・・・，ｓ_Ｋ｝を考える。トリップデータは、各地点における出発イベント、及び返却イベントの系列とみなすことができる。各々の出発イベントを出発時刻と到着地点との組（ｔ_ｉ,ｖ_ｉ）で定義する。 The travel time for each trip is defined by Δ≡τ−t. Now, a dataset consisting of n bike trips using the bike sharing system

Consider a set consisting of K bike points (hereinafter simply referred to as "points"), S = {s ₁ , ..., s _K}. Trip data can be regarded as a series of departure events and return events at each point. Each of the starting event is defined by a combination of a point of arrival and departure time (t _i, v _i).

と表せる。 The return event is defined at _{the return time τ i.} The sequence of return events at stations is

Can be expressed as.

The trip history storage device 12 may be configured by a Web server that holds a Web page, a database server that includes a database, and the like.

On the other hand, the external information storage device 14 of the present embodiment stores external information 15 that can be analyzed by the trip prediction device 10. The external information storage device 14 reads the external information 15 in accordance with the request from the trip prediction device 10, and transmits the read external information 15 to the trip prediction device 10. The external information 15 is data related to external factors that affect the trip, and may be, for example, weather or geographic information. The weather in this case includes fine rain, temperature, precipitation, humidity, and the like. Moreover, as the geographical information, the geographical distance between the regional pairs and the like can be mentioned.

FIG. 3 shows an example of the external information 15 of the present embodiment. The external information 15 shown in FIG. 3 shows, as an example, a case where the weather has information on the temperature and precipitation for each time. In the external information 15 shown in FIG. 3, the weather W _{t at} each time t is represented by a tuple W _t = (F _t , R _t ) consisting of the air temperature F _t and the precipitation R _t.

The external information storage device 14 may be configured by a Web server that holds a Web page, a database server that includes a database, and the like.

On the other hand, as shown in FIG. 1, the trip prediction device 10 of the present embodiment includes an operation unit 20, a search unit 22, a parameter estimation device 24, a parameter storage unit 30, a prediction unit 32, and an output unit 34. The trip prediction device 10 of the present embodiment stores a CPU (Central Processing Unit), a RAM (Random Access Memory), a program for executing each processing routine described later, and various data (Read Only Memory). Can be configured with a computer that includes. Specifically, the CPU that executes the above program functions as the parameter estimation device 24 and the prediction unit 32 of the trip prediction device 10 shown in FIG.

The operation unit 20 receives various operations from the user on the data of the trip history storage device 12 and the external information storage device 14. The various operations are operations such as registering, modifying, and deleting stored information. Information corresponding to various operations received by the operation unit 20 is output to the trip history storage device 12 and the external information storage device 14.

The input means of the operation unit 20 may be any one such as a keyboard, a mouse, a menu screen, and a touch panel. The operation unit 20 can be realized by a device driver of an input means such as a mouse or control software of a menu screen.

The search unit 22 receives information on the time and place to be predicted from the user via the input means. For example, it accepts information on the departure time and departure point to be predicted. The information on the time and place to be predicted received by the search unit 22 is output to the prediction unit 32.

The input means of the search unit 22 may be any one such as a keyboard, a mouse, a menu screen, and a touch panel. The search unit 22 can be realized by a device driver of an input means such as a mouse or control software of a menu screen.

The parameter estimation device 24 learns the relationship between the trip demand and the external factor based on the trip history information 13 stored in the trip history storage device 12 and the external information 15 stored in the external information storage device 14. It is a device. As shown in FIG. 1, the parameter estimation device 24 of the present embodiment includes two modules, a departure model 26 and a trip time model 28. The parameter estimation device 24 of the present embodiment estimates each parameter (details will be described later) that optimizes the departure model 26 and the trip time model 28, and outputs the estimation result to the parameter storage unit 30. The parameter estimation device 24 performs the above estimation by optimizing each parameter.

The departure model 26 of the present embodiment is a model of the departure event, and is learned by using the trip data based on the trip history information 13 and the weather data based on the external information 15. In the present embodiment, the learning procedure will be described using the trip history information 13 and the external information 15 described above.

・・・（１） The departure model 26 models a departure event at any point using a point process. First, the strength function is designed according to the general point process model procedure. The intensity function is a function that expresses the probability that an event will be generated per unit time. An example is shown below. The frequency of departure events varies with time and weather. _{Therefore, the intensity function λ u} (t, v | W _t ) of the departure event at the point u is introduced. As shown in the following equation (1), the intensity function λ _u (t, v | W _{t ) is a function λ u} (t | W _t ) representing the frequency with which a user departs from the point u at time t. _{It can be decomposed into a function fu} (v | t) that expresses the probability that the user who departs at time t heads for the point v.

... (1)

を用いて次式で定義すると、下記（２）式で表される。

・・・（２） A function _{that expresses the popularity of the function fu} (v | t) as the arrival point of the point v.

When defined by the following equation using, it is expressed by the following equation (2).

... (2)

・・・（３） On the other hand, the function λ _u (t | W _t ) can be decomposed into a time-dependent term and a weather-dependent term as shown in the following equation (3).

... (3)

を、さらに下記（４）式に示すように、トレンド項と周期項とに分解する。

・・・（４） It is a time-dependent term in the above equation (3).

Is further decomposed into a trend term and a periodic term as shown in the following equation (4).

... (4)

The trend term of the above equation (4) is modeled by the following equation (5), and the periodic term is modeled by the following equation (6).

In the above equation (5), a trend term that changes linearly with time is set. By modeling the trend term in this way, it is possible to capture the phenomenon in which demand increases or decreases linearly with time.

On the other hand, the periodic term is modeled by superimposing kernel functions as shown in the above equation (6). By modeling the periodic term in this way, it is possible to capture a periodic pattern that is non-linear with respect to time. According to the cycle term, for example, a sharp increase and decrease in trip demand during the morning and evening commuting hours can be modeled.

は、気温Ｆ_ｔと降水量Ｒ_ｔとを使って、下記（７）式の通りに定義する。

・・・（７） On the other hand, it is a term that depends on the weather in the above equation (3).

Is defined by the following equation (7) using the temperature F _t and the precipitation R _t.

... (7)

In the above equation (7), x _j , w _j , σ, a, b, c, d, and e are model parameters.

・・・（８） The likelihood of this model can be expressed as the following equation (8).

... (8)

When training the starting model 26, a set of parameters x _j , w _j , a, b, c, d that minimizes the likelihood L is estimated. Any method may be used for optimizing the parameters. Since the likelihood of the above equation (8) is differentiable for all parameters, the parameters may be optimized by using, for example, the gradient method.

・・・（９） On the other hand, the trip time model 28 models a change in the trip time, and is trained using the trip data. As an example, in the present embodiment, a case where the trip time changes depending on the auxiliary information m is considered. Assume according to | _{(m i Δ i)} trip time delta _i between the point u and the point v in the auxiliary information _{m i} is the probability distribution _{p uv.} Any probability distribution may be used for modeling the trip time, but in the present embodiment, a case where a lognormal distribution is used will be described. The probability distribution of this embodiment is expressed by the following equation (9).

... (9)

を推定する。ここで、Ｍは補助情報ｍ_ｉの集合である。 In the above equation (9), the parameter estimation device 24 uses the maximum likelihood method or the like according to the general procedure for estimating the parameters of the probability density distribution.

To estimate. Here, M is a set of auxiliary information m _i.

The parameter storage unit 30 stores a set of optimum parameters obtained as an estimation result of the parameter estimation device 24.

The parameter storage unit 30 may be any as long as the set of parameters estimated by the parameter estimation device 24 is stored and can be restored. The parameter storage unit 30 may be configured as, for example, a database, or may be configured as a specific area of a general-purpose storage device (memory, hard disk device, etc.) provided in advance.

The prediction unit 32 predicts the trip at the time to be predicted by using the departure model 26 and the trip time model 28 based on the estimation result of the parameter estimation device 24. Information on the time and place to be predicted is input from the search unit 22 to the prediction unit 32, and a set of parameters estimated by the parameter estimation device 24 is input from the parameter storage unit 30. Further, the prediction unit 32 outputs the trip prediction result to the output unit 34. For example, at the departure time of the prediction target, the arrival point when the departure point of the prediction target is departed is predicted by using the departure model 26, and the trip time between the departure point of the prediction target and the predicted arrival point is tripped. The time model 28 is used to make a prediction for each auxiliary information, and the arrival time is predicted from the predicted trip time.

Although there are a plurality of methods for simulating a point process in trip prediction, for example, a method called "thinning" (see Non-Patent Document 4) can be applied.
OGATA, Yosihiko. On Lewis' simulation method for point processes. IEEE Transactionson Information Theory, 1981, 27.1: 23-31.

The output unit 34 receives a prediction result from the prediction unit 32 and outputs the input prediction result. The "output" in the output unit 34 is a general term for concepts including display on a display, printing on a printer, output of audio, transmission to an external device of the trip prediction device 10, and the like. The output unit 34 may or may not include an output device such as a display or a speaker, and may have a form suitable for the output method. The output unit 34 can be realized by the driver software of the output device, the driver software of the output device, the output device, or the like.

<Operation of trip prediction device>
Next, the operation of the trip prediction device 10 of the present embodiment will be described.

<Parameter estimation routine>
First, when the trip history information 13 is input by the operation unit 20, the trip prediction device 10 stores the input trip history information 13 in the trip history storage device 12. Further, when the external information 15 is input by the operation unit 20, the trip prediction device 10 stores the input external information 15 in the external information storage device 14.

The parameter estimation device 24 of the trip prediction device 10 executes the parameter estimation routine shown in FIG. 4 as an example.

As shown in FIG. 4, in step S100, the parameter estimation device 24 uses the trip history information 13 and the external information 15 to obtain parameters that minimize the likelihood L of the above equation (8) as described above. The parameters of the starting model 26 are optimized by estimating the set x _j , w _{j, a, b, c, d.}

Parameter estimation unit 24 in the next step S102, using the trip history information 13, as described above, the probability expressed by the equation (9) distribution _{p uv} | estimating the parameters (delta _{i m i)} In, the parameters of the trip time model 28 are optimized.

The processing order of steps S100 and S102 is not particularly limited, and it goes without saying that the order may be the reverse of that of the present embodiment.

In the next step S104, the parameter estimation device 24 outputs the set of parameters optimized in steps S100 and S102 to the parameter storage unit 30, and ends the parameter estimation routine. By this process, the parameter storage unit 30 stores the optimized set of parameters.

<Trip prediction routine>
Next, the trip prediction routine of this embodiment will be described.

After the parameter estimation routine is executed and the set of parameters optimized by the parameter estimation device 24 is stored in the parameter storage unit 30, the search unit 22 sets the time to be predicted by the user via the input means. When the location information is received, the trip prediction device 10 executes the trip prediction routine shown in FIG. 5 as an example.

As shown in FIG. 5, in step S150, the prediction unit 32 acquires the above-mentioned optimized parameter set from the parameter storage unit 30.

In the next step S152, the prediction unit 32 uses the departure model 26 and the trip time model 28 optimized according to the set of parameters acquired in the step S150, and predicts the prediction target (arbitrary point) input from the search unit 22. ), Predicts future trips and outputs the prediction result.

In the next step S154, the output unit 34 outputs the prediction result of the prediction unit 32 and ends the trip prediction routine.

As described above, the parameter estimation device 24 of the trip prediction device 10 of the present embodiment uses the trip history information 13 and the external information 15 that affects the trip to depart and arrive at arbitrary points. A parameter that optimizes the departure model 26, which is a departure model in which the departure event defined in the set with is modeled using a point process model and is represented by an intensity function representing the probability that the departure event is generated per unit time. Is a device that estimates parameters using the trip history information 13 to optimize the trip time model 28 that has learned the change in trip time from the departure point to the arrival point for each arbitrary point.

As described above, in the trip prediction device 10 of the present embodiment, by using the departure model 26 and the trip time model 28, four elements (temporal periodicity, trend, external information such as weather, etc.) that affect the trip are used. And the information associated with each trip) is taken into consideration, which enables highly accurate prediction of trips.

In addition, the intensity function in this embodiment has a time-dependent term including a trend term which is a term modeled by changing linearly with time. By modeling the trend term in this way, according to the parameter estimation device 24 of the present embodiment, it is possible to capture the phenomenon that the demand linearly increases or decreases with the change of time.

Further, the intensity function in the present embodiment has a time-dependent term including a periodic term which is a term modeled by superposition of kernel functions. By modeling the periodic term in this way, according to the parameter estimation device 24 of the present embodiment, it is possible to capture a periodic pattern that is non-linear with respect to time.

It should be noted that this embodiment is an example, and the specific configuration is not limited to this embodiment, but includes a design and the like within a range that does not deviate from the gist of the present invention, and may be changed depending on the situation. Needless to say.

The trip prediction device 10 of the present embodiment has a computer system inside, but the "computer system" is a homepage providing environment (or display) when a WWW (World Wide Web) system is used. Environment) shall also be included.

Further, in the present embodiment, the mode in which the program is pre-installed has been described, but the program can be stored in a computer-readable recording medium and provided, or provided via a network. Is also possible.

10 Trip Predictor 24 Parameter Estimator 26 Departure Model 28 Trip Time Model 32 Predictor

Claims (8)

It is a departure model that uses a point process model to model a departure event defined by a set of a departure time and an arrival point for each arbitrary point using trip history information and external information that affects the trip. Then, the parameters of the departure model expressed by the intensity function representing the probability that the departure event is generated per unit time are estimated so as to optimize the likelihood expressed by using the intensity function of the departure model.
Using the trip history information, the parameters of the trip time model representing the probability distribution of the trip time from the departure point to the arrival point for each arbitrary point are estimated by using the maximum likelihood method.
A parameter estimation device,
The external information includes weather data W _t at time t.
The intensity function includes a function λ _u (t | W _t ) representing the frequency with which a user departs from the point u at time t, and a function f f representing the probability that a user departing from point u at time t heads for point v. _{It is expressed using u} (v | t), and the function λ _u (t | W _t ) is expressed using a term that depends on the time t and a term that depends on the weather data W _t.
Parameter estimator . The time-dependent term of the intensity function includes a trend term, which is a term modeled by changing linearly with time .
The parameter estimation device according to claim 1. The time-dependent term of the intensity function includes a periodic term, which is a term modeled by the superposition of kernel functions .
The parameter estimation device according to claim 1 or 2. The parameters for optimizing the trip time model are estimated according to the probability distribution of the trip time between arbitrary points for each auxiliary information included in the trip history information.
The parameter estimation device according to any one of claims 1 to 3. A departure model optimized by the parameters estimated by the parameter estimation device according to any one of claims 1 to 4, and a trip time model optimized by the parameters estimated by the parameter estimation device. Equipped with a predictor that predicts future trips at any point based on
Trip predictor. The parameter estimator uses the trip history information and external information that affects the trip to mark the departure event defined by the combination of the departure time and the arrival point at any point with the arrival time as the mark. Using a point process, we estimate the parameters that optimize the modeled departure model by expressing it as an intensity function that represents the probability that the departure event will occur per unit time.
Using the trip history information, estimate the parameters that optimize the trip time model that learned the change in trip time.
It is a parameter estimation method .
The external information includes weather data W _t at time t.
The intensity function includes a function λ _u (t | W _t ) representing the frequency with which a user departs from the point u at time t, and a function f f representing the probability that a user departing from point u at time t heads for point v. _{It is expressed using u} (v | t), and the function λ _u (t | W _t ) is expressed using a term that depends on the time t and a term that depends on the weather data W _t.
Parameter estimation method . The trip predictor is based on a departure model optimized by the parameters estimated by the parameter estimation method according to claim 6 and a trip time model optimized by the parameters estimated by the parameter estimation method. Predict future trips at any point,
How to predict trips. A program for causing a computer to function as the parameter estimation device according to any one of claims 1 to 4.

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